Copy files that have at least the mention of one certain word

I want to look through 100K+ text files from a directory and copy to another directory only the ones which contain at least one word from a list.

I tried doing an if statement with grep and cp but I have no idea how to make it to work this way.

for filename in *.txt 
do 
grep -o -i "cultiv" "protec" "agricult" $filename|wc -w 
if [ wc -gt 0 ]
then cp $filename ~/desktop/filepath
fi 
done

Obviously this does not work but I have no idea how to store the wc result and then compare it to 0 and only act on those files.